Uniform electric field of magnitude `100 V//m` in space is directed along the line `y=3+x`. Find the potential difference between point `A (3, 1)` & `B(1, 3)`

Options

A. `100 V`
B. `200 sqrt(2) V`
C. `200 V`
D. `0`

Answer

D

Explanation

Slope from x axis
`y=3+x, tan theta=1 rArr theta=45^(@)`
`:.` Electric field in vector from `vec(E)=100((hat(i)+hat(j))/sqrt(2))`
`:. V=-underset(("3, 1"))overset(("1, 3"))(int)vec(E).dvec(r)`
`V=(-100)/sqrt(2)[underset(3)overset(1)(int)dx+underset(1)overset(3)(int) dy]=50 sqrt(2)[-2+2]=0`
Alternate solution: The direction of electric field and the slope of line A (3, 1) & (1, 3) is `bot` to each others so the dot product `vec(E).dvec(r)` becomes zero.